There is no special type for ($). The name is simply special cased in the compiler. The rule is something like:

Whenever you see: f Prelude.$ x instead try to type check: f x That may not be the exact behavior, but it's close. To fix (.) (in a similar fashion) you would have to have a similar rule, like: Whenever you see: f Prelude.. g instead try to type check: \x -> f (g x) -- Dan On Tue, Feb 10, 2015 at 6:19 PM, Tyson Whitehead <twhiteh...@gmail.com> wrote: > On February 10, 2015 16:28:56 Dan Doel wrote: > > Impredicativity, with regard to type theories, generally refers to types > > being able to quantify over the collection of types that they are then a > > part of. So, the judgment: > > > > (forall (a :: *). a -> a) :: * > > > > is impredicative, because we have a type in * that quantifies over all > > types in *, which includes itself. Impredicativity in general refers to > > this sort of (mildly) self-referential definition. > > Thanks Dan and David, > > That was informative. Also very interesting that ($) is a special case. > I tried this > > newtype Wrap = Wrap { extract :: forall f. Functor f => f Int } > > trip'' :: Wrap -> Wrap > trip'' a = Wrap $ extract a > > and the compiler was happy. Wrapping ($) as ($') gave an error as you > implied it would > > trip''' :: Wrap -> Wrap > trip''' a = Wrap $' extract a > where ($') = ($) > > With regard to my earlier comment about translating the (.) version > > trip' :: Wrap -> Wrap > trip' = Wrap . extract > > to core, I can see it's actually okay. A most you may need is a lambda to > float the implicit parameters backwards > > trip' :: Wrap -> Wrap > trip' = Wrap . (\a f fDict -> extract f fDict a) > > as GHC seems to always float them as far leftward as possible > > extract :: Functor f => Wrap -> f Int > > I take it there are no user supplied types a person can give to overcome > the predicative assumption? > > Out of curiosity, how would you write the special internal type that ($) > has that separates it from ($') above? > > Thanks! -Tyson >

_______________________________________________ Haskell mailing list Haskell@haskell.org http://www.haskell.org/mailman/listinfo/haskell